The notation lim x→af(x)=L is read​ "the ____ of​ ___ as​ ____ approaches​ ___ equals the number​ ___."

Q: 4x +1 - 3 To evaluate lim X- 2 -, this has to be transformed. Which of the statements below is…

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Q: x2 - 4 Let f1x2 X - 2 a. Calculate f1x2 for each value of x in the following table. x² - 4 b. Make a…

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Q: The graph of a function f is shown in the figure above. Which of the following limf(x) = 1 %3D o lim…

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Q: x approaches 9, f(x) approaches 4, but f(9) = 2. As x approaches 9, f(x) approaches 2, but f(9) = 4.…

A: Given query is to determine the correct information for the limit property.

Q: x-4 Evaluate: lim x-4 x2-x-12

A: use L'Hospital Rule or solve it simply.

Q: lim f(x) = 5 and_lim_f(x)=5, but f(3) does not exist. X-3 X-3* What can you say about lim f(x)? X-3…

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Q: 74-14a? Let f (x) The 425+2 lim,-0 f (x)= [0].

A: Need to find limit f(x) as given

Q: If lim f(x) = -5, lim f(æ) = 2, lim g(x) = -1, and lim g(x) = 4, then the limit lim (2f(x) – 39(x) +…

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Q: c. The value of lim f(x) does not exist if f(a) is undefined. Xa O A. This statement is false…

A: Given that

Q: Question * If lim x-1 f(x)-f(1)-3, then lim A->0 x-1 ƒ(1+h)-f(1)_3. h

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Q: f'(x) = (x-1)(x-2)(x-3)(x-4)   What can be said about lim(x->infinity) if anything

A: Answer and explanation is given below

Q: 2 -x Evaluate lim x-2 x5 - 32 1/-60 O 1/80 O NONE OF THESE -80 O -1/80

A: The given limit,                 limx→22-xx5-32

Q: the blank: For any positive integer n, lim as x goes to infinity of x^n / e^x =_____

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Q: x2-16 x - 16 Let f(x) = (a) Calculate f(x) for each value of x in the following table. (b) Make a…

A: This question can be solved using the concept of limits.

Q: x³-343 Use scratch paper to complete the table below, and guess the value of the limx→7 240: f(x)…

A: The limit of a function f(x) is found by putting the values of x Put the different values of x in…

Q: a/Limit of a function Lim A = 0 B = 1 O 3 €3¾/1 x²+2x-1 X 3+3X² 3

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Q: Consider the function g graphed in the accompanying figure. For what values of -3 < xo < 2 does lim…

A: Consider the given graph: For a function to have its limit to exist at a point, Left hand limit and…

Q: Fina the llmit or State that the lmit does not exist li Lim (I+ * 2. Lim (I+2X)

A: Explanation of the answer is as follows

Q: ak+1 If lim k→+∞ ak = 5, then ak diverges. k=1

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Q: The floor function For any real number x, the floor function (UI greatest integer function) [x] is…

A: limx→-1-x=-2     Because, x=-2 for all x∈[-2, -1)limx→-1+x=-1     Because, x=-1 for all x∈[-1, 0)

Q: Given that: lim lim I →→ 8 I→ 8 f(x) = 2, lim 2. f(x) = g(x) h(x) = I-8 g(x) = = - 3, and lim I-8…

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Q: The ceiling function For any real number x, the ceiling function <x= is the smallest integer greater…

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Q: x2 -9 Let f(x) = x² -9 (a) Calculate f(x) for each value of x in the following table. (b) Make a…

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Q: If lim f(x) = 6, lim f(x) = 6, and f(3) = 0, then X-3* X-3" O A. lim f(x) does not exist X-3 O B.…

A: Here, given that limx→3+f(x)=6, limx→3-f(x)=6 That is limx→3+f(x)=limx→3-f(x)=6 Hence, limx→3f(x)=6

Q: ³f(x)-2g(x) is ... If lim f (x) = 2 and lim g(x)=-1, then lim- f (x)+ g(x) xa

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Q: Evaluate the lim h->0 (f'(5+h)-f'(5))/h

A: Given limit is : limh→0f'5+h-f5h To find the value of the limit.

Q: If lim an = 0, then the answer to lim a, is Answer:

A: Please solve two small question

Q: (a) lim f(x)= (b) lim,-2+ f(x) = (c) lim f(x) =, (d) Is f'(3) is positive, negative, or zero? (e) Is…

A: We will solve the problem

Q: [7-x if r5 The function f is defined for all real numbers, as shown above. What is the value of the…

A: Solution: The objective is to find the given limit value

Q: 5 A functionf is defined by x+1. x<2 f(x)=2x+5, 25x<4 x2-4, x24 Sketch the graph of y f(x). (a) Find…

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Q: f x^n / e^x =__

A: lim as x goes to infinity of x^n / e^x = 0

Q: b2 - a2 Prove that x dx = lim b- a n- 00 b - a + a(b – a) (1) + (6 – a)² ( = lim n² (b - a)2 n2 =…

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Q: Find all values of p so that lim x->2 (px^2+ 15x+ 15 +p/x^2+x-2 )exists

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Q: 1-x , and lim 1-x 1-x Evaluate lim 2x X00 lim 2x X- 00 X X00 1-x lim 2x (Simplify your answer.) 1-x…

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Q: n2 Find lim if it exists. Be sure to show all of your work. n-00 en 2.

A: topic -limits

Q: Calculate the following limits using the factorization formula

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Q: If lim f(x) = 17 and lim g(x) = 24 then lim[3f(x)g(x) – 8] - x→2 x→2 x→2 243 34 1216 1224 1232

A: Limit of the function

Q: Question: What is lim h(x)? x--2 x< - 2 -2<x< 2 x2 2 -2x – 1 h(x) = {x | 2x – 3

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Q: 3x* - 4x2 +3x – 6 Evaluate lim x-0 5x- x2 – 3x5-2x -1 does not exist O 1 O None of these

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Q: The greatest integer function, also known as the floor function, isdefined by [ x ] = n, where n is…

A: Consider the given function, y=x draw the table of points, x y 0&lt;x&lt;1 0 1&lt;x&lt;2 1…

Q: 4. Sketch a function f such that: lim f(x) and f(4) exist and are equal to one another. x→4 5.…

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Q: x²-125 Use scratch paper to complete the table below, and guess the value of the lim,→5 x²–25 * f(x)…

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Q: 53. (a) If the symbol |[ ] denotes the greatest integer function defined in Example 10, evaluate…

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Q: limit, if it exists. 5X +8 x--4x - 7 ree of the numerator is equal to equal to the degree of the…

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Q: Prove that lim (5x + 2) = 17. What you have to do is to assume a given (but unknown) ɛ, then pluck a…

A: We have to prove the limit                                             limx→35x+2=17

Q: Question: The table shows values of k(x). What is lim k(x)? x->-5- -5.1 -5.01 -5.0001 -5 -4.999…

A: Given:

Q: If lim f(x) =L and lim f(x) = M, where L and M are finite real numbers, then what must be true about…

A: Option B is correct

Q: flIth)-f(1) find lim.

A: Given query is to find the Indicated expression.

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.